Completely positive matrices Abraham Berman, Naomi Shaked-Monderer.

By:

Berman, Abraham

Contributor(s):

Shaked-Monderer, Naomi

Material type: Text

TextLanguage: English Publication details: [River Edge] New Jersey : World Scienfic, c2003.Description: 1 online resource (ix, 206 p.) : ill. ; 24 cmSubject(s):

Matrices

DDC classification:

512.943 BER

Online resources:

Click here to access online

Contents:

Preliminaries: Matrix Theoretic Background Positive Semidefinite Matrices Nonnegative Matrices and M-Matrices Schur Complements Graphs Convex Cones The PSD Completion Problem Complete Positivity: Definition and Basic Properties Cones of Completely Positive Matrices Small Matrices Complete Positivity and the Comparison Matrix Completely Positive Graphs Completely Positive Matrices Whose Graphs are Not Completely Positive Square Factorizations Functions of Completely Positive Matrices The CP Completion Problem CP Rank: Definition and Basic Results Completely Positive Matrices of a Given Rank Completely Positive Matrices of a Given Order When is the CP-Rank Equal to the Rank?

In: ebrarySummary: A real matrix is positive semidefinite if it can be decomposed as A=BB′. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB′ is known as the cp-rank of A. This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Project book	CUTN Central Library	512.943 BER (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48821

Includes bibliographical references (p. 193-197) and index.

Preliminaries:
Matrix Theoretic Background
Positive Semidefinite Matrices
Nonnegative Matrices and M-Matrices
Schur Complements
Graphs
Convex Cones
The PSD Completion Problem
Complete Positivity:
Definition and Basic Properties
Cones of Completely Positive Matrices
Small Matrices
Complete Positivity and the Comparison Matrix
Completely Positive Graphs
Completely Positive Matrices Whose Graphs are Not Completely Positive
Square Factorizations
Functions of Completely Positive Matrices
The CP Completion Problem
CP Rank:
Definition and Basic Results
Completely Positive Matrices of a Given Rank
Completely Positive Matrices of a Given Order
When is the CP-Rank Equal to the Rank?

Online version restricted to NUS staff and students only through NUSNET.

A real matrix is positive semidefinite if it can be decomposed as A=BB′. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB′ is known as the cp-rank of A.

This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.

Mode of access: World Wide Web.

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